I am just back from Jordan and thanks to all the advises received here, my trip was marvellous.
I have travelled alone, with my rucksack, during 10 days.
The 1st day, from Amman, I have visited Jerash and Aijun (I took the public bus:no problem !): 2 beautiful places.
The 2d day, I have hired a taxi and have been to the dead see, Mount Nebo, Metaba, Kerak and Petra. Unfortunaly, I had no time to go to Dana.
I have spent 3 nights and 2 days in Petra, visiting all the parts of this marvellous site; I have "climbed" almost 2500 steps, arriving very soon at 7h30, the perfect hour when there is nobody. I could go out the Sihk and discover the tresaury without anybody before me: alone, magical ! And I was at 9 at the Monastry, with only 1 or 2 other people.
With the bus, I transfered to Wadi Rum where the guide I had hired was waiting for me. I spent 3 nigts and 4 days in the desert, sleeping in a bedouin camp and hiking and climbing all the time. All was perfect: the landscapes, the meals cooked on the wood fire, the guide so welcoming and caring, the sunset, the stars in the sky, the temperature even at night (under my 2 blankets), the evenings with bedouin music (oud= sort of guitar) and songs. Even the break down of the 4x4 in the desert was excited, without any mobile network but thnks a solid solidarity between Bedouins...
The guide let me in Aqaba, where I stayed 2 nights and 1 day. Maybe the interesting part of my trip. But I rested on the beach: my knees were so painfull !
I took the bus from Aqaba to Amman, my last afternoon there, I visited the Nympheus, the Theater, the Citadel and made some shopping.
The revisited too the 2 little restaurants where I had eaten the first 2 days: very simple, few foreigners, delicious and a bill of 2 JD only.
You have unterstood: this trip was perfect. I wish you the same experience !